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Simplifying 5x2 = 3.6 + 4.7x Solving 5x2 = 3.6 + 4.7x Solving for variable 'x'. Reorder the terms: -3.6 + -4.7x + 5x2 = 3.6 + 4.7x + -3.6 + -4.7x Reorder the terms: -3.6 + -4.7x + 5x2 = 3.6 + -3.6 + 4.7x + -4.7x Combine like terms: 3.6 + -3.6 = 0.0 -3.6 + -4.7x + 5x2 = 0.0 + 4.7x + -4.7x -3.6 + -4.7x + 5x2 = 4.7x + -4.7x Combine like terms: 4.7x + -4.7x = 0.0 -3.6 + -4.7x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.72 + -0.94x + x2 = 0.0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + -0.94x + 0.72 + x2 = 0.0 + 0.72 Reorder the terms: -0.72 + 0.72 + -0.94x + x2 = 0.0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + -0.94x + x2 = 0.0 + 0.72 -0.94x + x2 = 0.0 + 0.72 Combine like terms: 0.0 + 0.72 = 0.72 -0.94x + x2 = 0.72 The x term is -0.94x. Take half its coefficient (-0.47). Square it (0.2209) and add it to both sides. Add '0.2209' to each side of the equation. -0.94x + 0.2209 + x2 = 0.72 + 0.2209 Reorder the terms: 0.2209 + -0.94x + x2 = 0.72 + 0.2209 Combine like terms: 0.72 + 0.2209 = 0.9409 0.2209 + -0.94x + x2 = 0.9409 Factor a perfect square on the left side: (x + -0.47)(x + -0.47) = 0.9409 Calculate the square root of the right side: 0.97 Break this problem into two subproblems by setting (x + -0.47) equal to 0.97 and -0.97.Subproblem 1
x + -0.47 = 0.97 Simplifying x + -0.47 = 0.97 Reorder the terms: -0.47 + x = 0.97 Solving -0.47 + x = 0.97 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.47' to each side of the equation. -0.47 + 0.47 + x = 0.97 + 0.47 Combine like terms: -0.47 + 0.47 = 0.00 0.00 + x = 0.97 + 0.47 x = 0.97 + 0.47 Combine like terms: 0.97 + 0.47 = 1.44 x = 1.44 Simplifying x = 1.44Subproblem 2
x + -0.47 = -0.97 Simplifying x + -0.47 = -0.97 Reorder the terms: -0.47 + x = -0.97 Solving -0.47 + x = -0.97 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.47' to each side of the equation. -0.47 + 0.47 + x = -0.97 + 0.47 Combine like terms: -0.47 + 0.47 = 0.00 0.00 + x = -0.97 + 0.47 x = -0.97 + 0.47 Combine like terms: -0.97 + 0.47 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.44, -0.5}
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